iOS Share Extension: pick the destination inside the share sheet

SwiftUI folder picker in the extension (WebDAV PROPFIND), account shared via
a Keychain group, upload on a background session that outlives the extension
and is finished by the app. The inbox + notification hand-off remains as the
fallback (no account / 'choose later'). Shared code moves to ios/Shared.

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>

ios/Shared/TransferTypes.swift

@@ -0,0 +1,67 @@
+import Foundation
+
+/// What a background upload/download task is, stored in the task's
+/// `taskDescription` so it's still known if the app was relaunched by the
+/// system to deliver the result - possibly for a task the Share Extension
+/// started. Compiled into both targets.
+struct TransferTaskInfo: Codable {
+  enum Kind: String, Codable { case upload, download }
+
+  let kind: Kind
+  let batch: String
+  let name: String
+  let remoteFolder: String?
+  /// A file to delete once the task ends (the upload's staged copy).
+  let stagedPath: String?
+}
+
+/// Running totals for one "upload these 3 files" / "download these 2 files"
+/// request, so the one summary notification (and the Dart-side "folder
+/// changed" event) fires exactly once, on the last file.
+struct TransferBatch: Codable {
+  let kind: TransferTaskInfo.Kind
+  let remoteFolder: String?
+  let total: Int
+  var succeeded: Int
+  var failed: Int
+
+  var finished: Int { succeeded + failed }
+}
+
+/// Persists [TransferBatch]es in the App Group's `UserDefaults`, not the
+/// process's own: the Share Extension starts an upload batch, and the app -
+/// a different process, possibly relaunched in the background - finishes
+/// counting it.
+enum TransferBatchStore {
+  private static let lock = NSLock()
+
+  private static var defaults: UserDefaults {
+    UserDefaults(suiteName: AppGroup.identifier) ?? .standard
+  }
+
+  private static func key(_ id: String) -> String { "transfer.batch.\(id)" }
+
+  static func save(_ batch: TransferBatch, id: String) {
+    lock.lock()
+    defer { lock.unlock() }
+    if let data = try? JSONEncoder().encode(batch) { defaults.set(data, forKey: key(id)) }
+  }
+
+  /// Counts one file's outcome. Returns the batch when that was its last
+  /// file (and forgets it), nil while others are still running.
+  static func record(_ info: TransferTaskInfo, success: Bool) -> TransferBatch? {
+    lock.lock()
+    defer { lock.unlock() }
+    let storageKey = key(info.batch)
+    var batch =
+      defaults.data(forKey: storageKey).flatMap { try? JSONDecoder().decode(TransferBatch.self, from: $0) }
+      ?? TransferBatch(kind: info.kind, remoteFolder: info.remoteFolder, total: 1, succeeded: 0, failed: 0)
+    if success { batch.succeeded += 1 } else { batch.failed += 1 }
+    if batch.finished >= batch.total {
+      defaults.removeObject(forKey: storageKey)
+      return batch
+    }
+    if let data = try? JSONEncoder().encode(batch) { defaults.set(data, forKey: storageKey) }
+    return nil
+  }
+}